Laser spectroscopy outperforms electrochemical and semiconductor gas sensors in selectivity and environmental survivability. However, the performance of the state-of-the-art laser sensors is still insufficient for many high precision applications. Here, we report mode-phase-difference photothermal spectroscopy with a dual-mode anti-resonant hollow-core optical fiber and demonstrate all-fiber gas (acetylene) detection down to ppt (parts-per-trillion) and <1% instability over a period of 3 hours. An anti-resonant hollow-core fiber could be designed to transmit light signals over a broad wavelength range from visible to infrared, covering molecular absorption lines of many important gases. This would enable multi-component gas detection with a single sensing element and pave the way for ultra-precision gas sensing for medical, environmental and industrial applications.